Antifragile Random Walks

A million timesteps with a Pareto distribution with $latex \alpha =1 $ and mode shifted down to $latex -11 $ from $latex 1 $. Notice how for most time steps, the walk moves downward. However, the rarer upticks are large, orders of magnitude larger than downward movements.

In [1]:
T = 1000000
X = np.zeros(T)

for i in range(5):
    for t in range(T-1):
        X[t+1] = X[t] + np.random.pareto(1) - 12

    plt.plot(X)
    plt.show()

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